$\newcommand{\d}{\mathbf d}\newcommand{\one}{\mathbf 1}\newcommand{\E}{\operatorname{E}}\newcommand{\Var}{\operatorname{Var}}$In this post I’m going to look at the degree distribution of stochastic block models. $n$ will denote…
$\newcommand{\X}{\mathcal X}\newcommand{\x}{\mathbf x}\newcommand{\0}{\mathbf 0}\newcommand{\one}{\mathbf 1}\newcommand{\y}{\mathbf y}\newcommand{\z}{\mathbf z}$In this post I’m going to look at distributions over polynomials using Gaussian processes.…
$\newcommand{\Om}{\Omega}\newcommand{\F}{\mathscr F}\newcommand{\one}{\mathbf 1}\newcommand{\R}{\mathbb R}\newcommand{\e}{\varepsilon}\newcommand{\E}{\operatorname{E}}\newcommand{\Var}{\operatorname{Var}}\newcommand{\convas}{\stackrel{\text{a.s.}}{\to}}\newcommand{\w}{\omega}\newcommand{\N}{\mathbb N}\newcommand{\convp}{\stackrel{\text{p}}{\to}}$In this post I’m going to introduce almost sure convergence for sequences of random variables, compare…
$\newcommand{\E}{\operatorname{E}}\newcommand{\Xmin}{X_{(1)}}\newcommand{\Fmin}{F_{(1)}}\newcommand{\fmin}{f_{(1)}}\newcommand{\eff}{\operatorname{eff}}$In this post I’m going to look at two probability questions that arose in the context of a friendly game…
$\newcommand{\Om}{\Omega}\newcommand{\w}{\omega}\newcommand{\F}{\mathscr F}\newcommand{\R}{\mathbb R}\newcommand{\e}{\varepsilon}\newcommand{\convd}{\stackrel{\text d}\to}\newcommand{\convp}{\stackrel{\text p}\to}\newcommand{\convas}{\stackrel{\text {a.s.}}\to}\newcommand{\E}{\operatorname{E}}\newcommand{\Var}{\operatorname{Var}}\newcommand{\one}{\mathbf 1}$In this post I’m going to introduce two modes of convergence for random variables.…
$\newcommand{\X}{\mathcal X}\newcommand{\one}{\mathbf 1}$In this post I’m going to look at the following: suppose I have a random variable $X$ supported…
$\newcommand{\one}{\mathbf 1}\newcommand{\convd}{\stackrel{\text d}\to}\newcommand{\convp}{\stackrel{\textp}\to}\newcommand{\p}{\mathbf p}\newcommand{\0}{\mathbf 0}\newcommand{\X}{\mathbf X}\newcommand{\Mult}{\text{Mult}}\newcommand{\E}{\operatorname{E}}\newcommand{\e}{\varepsilon}\newcommand{\Var}{\operatorname{Var}}\newcommand{\R}{\mathbb R}\newcommand{\rank}{\operatorname{rank}}\newcommand{\H}{\mathcal H}$Let $X$ be a continuous random vector in $\mathbb R^n$ with distribution $P_X$…
$\newcommand{\vp}{\varphi}$$\newcommand{\E}{\operatorname{E}}$$\newcommand{\Exp}{\operatorname{Exp}}$In this post I’ll take a look at wrapped distributions. If $X$ has a continuous distribution on $\mathbb R$ with…
$\newcommand{\F}{\mathscr F}$$\newcommand{\R}{\mathbb R}$$\newcommand{\A}{\mathscr A}$$\newcommand{\G}{\mathcal G}$$\newcommand{\E}{\operatorname E}$$\newcommand{\dp}{\,\text dP}$$\newcommand{\1}{\mathbf 1}$Let $(\Omega, \F, P)$ be a probability space and let $X : \Omega…
$\newcommand{\vp}{\varphi}$$\newcommand{\dmux}{\,\text d\mu(x)}$$\newcommand{\dmu}{\,\text d\mu}$$\newcommand{\E}{\operatorname{E}}$Let $\mu$ be a probability measure on $(\mathbb R, \mathbb B)$ where $\mathbb B$ is the Borel $\sigma$-algebra…